One thing I have with Intel is the virtual certainty the machine will work flawlessly with Linux. Atom, Celeron, Pentium, Core, and Xeon E3 have built-in GPUs that are very well supported.
Before jumping to AMD gear, I'd like to know if I'd have the same "just works" experience. I'm well past the age I liked to waste time debugging setups.
Ryzens do not have an integrated GPU, at least not at the moment. The CPU itself works out of the box, even slightly more exotic features like virtualization is flawless under KVM.
If you want a Ryzen-based desktop with "just works experience" similar to i7-based Intels, go with a Radeon RX460 or RX560 GPU. It will get picked up by the open source AMDGPU driver in the latest popular desktop distros.
I have a Ryzen 1700 with an RX460 (it was the cheapest card from the same supplier that would drive my screens) and its been flawless out the box with the open source radeon driver.
In fact I didn't have to touch any of the graphics at all, more by chance than anything left screen was left/right screen was right (it's 50/50 and I end up with it the wrong way around 95% of the time).
I'm driving 2x2560x1440 Dell's and it's buttery smooth.
I don't game on that machine (it's a work desktop I built).
The open source radeon driver has improved massively in the last year or two.
Well, it is bleeding edge and you probably know that linux needs some time to support that properly. The integrated graphics is a non-issue here: Neither X299 nor X399 processors have any. You have to combine them with a gpu, and then are free to chose one that is properly supported. For what it's worth, the RX line was the first gpu ever that had proper working free Linux drivers on release (but the stronger versions like the RX 570 or 580 are not in stock or overpriced, thus not a reasonable option right now).
I'd expect the RX 550 or any of the older AMD gpus with the mesa driver to be a good choice, but it depends on what you want to do.
RX 550 won't work without upgrading mesa either from source or from 3rd party repos [1]. I went with RX 460 instead and it worked flawlessly out of the box with Ubuntu 17.04
Before jumping to AMD gear, I'd like to know if I'd have the same "just works" experience. I'm well past the age I liked to waste time debugging setups.